Multivariate kernel smoothing and its applications

Content: Preface List of FiguresList of Tables List of Algorithms Introduction Exploratory data analysis with density estimation Exploratory data analysis with density derivatives estimation Clustering/Unsupervised learning Classification/Supervised learning Suggestions on how to read this monograph Density estimation Histogram density estimation Kernel density estimation Probability contours as multivariate quantiles Contour colour scales Gains from unconstrained bandwidth matrices Advice for practical bandwidth selection Squared error analysis Asymptotic squared error formulas Optimal bandwidths Convergence of density estimators Further mathematical analysis of density estimators Asymptotic expansion of the MISE Asymptotically optimal bandwidth Vector versus vector half parametrisations Bandwidth selectors for density estimation Normal scale bandwidths Maximal smoothing bandwidths Normal mixture bandwidths Unbiased cross validation bandwidths Biased cross validation bandwidths Plug in bandwidths Smoothed cross validation bandwidths Empirical comparison of bandwidth selectors Theoretical comparison of bandwidth selectors Further mathematical analysis of bandwidth selectors Relative convergence rates of bandwidth selectors Optimal pilot bandwidth selectors Convergence rates with data-based bandwidths Modified density estimation Variable bandwidth density estimators Balloon density estimators Sample point density estimators Bandwidth selectors for variable kernel estimation Transformation density estimators Boundary kernel density estimators Beta boundary kernels Linear boundary kernels Kernel choice Higher order kernels Further mathematical analysis of modified density estimators Asymptotic error for sample point variable bandwidthestimators Asymptotic error for linear boundary estimators Density derivative estimation Kernel density derivative estimators Density gradient estimators Density Hessian estimators General density derivative estimators Gains from unconstrained bandwidth matrices Advice for practical bandwidth selection Empirical comparison of bandwidths of different derivative orders Squared error analysis Bandwidth selection for density derivative estimators Normal scale bandwidths Normal mixture bandwidths Unbiased cross validation bandwidths Plug in bandwidths Smoothed cross validation bandwidths Convergence rates of bandwidth selectors Case study: the normal density Exact MISE Curvature matrix Asymptotic MISE Normal scale bandwidth Asymptotic MSE for curvature estimation Further mathematical analysis Taylor expansions for vector-valued functions Relationship between multivariate normal moments Applications related to density and density derivative estimationLevel set estimation Modal region and bump estimation Density support estimation Density-based clustering Stable/unstable manifolds Mean shift clustering Choice of the normalising matrix in the mean shift Density ridge estimation Feature significance Supplementary topics in data analysis Density difference estimation and significance testing Classification Density estimation for data measured with error Classical density deconvolution estimation Weighted density deconvolution estimation Manifold estimation Nearest neighbour estimation Further mathematical analysis Squared error analysis for deconvolution kernel density estimatorsOptimal selection of the number of nearest neighboursComputational algorithms R implementation Approximate binned estimation Approximate density estimation Approximate density derivative and functionalestimation Recursive normal density derivatives Recursive normal functionals Numerical optimisation over matrix spaces